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Crit Hit Calculation

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Created: 2019-10-01
Updated: 2020-05-17
https://forums.gearboxsoftware.com/t/guide-critical-hit-calculation/3761404


This guide explains the mechanics of critical hits.

I’ve spent a long time analysing and calculating and testing a ton of weapons and skill combinations etc. until I found the formulas that accurately predict everything I’ve tested. Only damage values below 10k have been used, and no larger difference than +- 1 between formula prediction and in-game result was tolerated.

 

## [color=white][u]**Content:**[/u][/color]

[color=white]1. Main formula without FL4K’s unique stuff
2. FL4K
2.1 Regular crit bonuses
2.2 PostAdd bonuses / Fade Away
3. Overkill (Guardian Rank)
4. Pull the Holy Pin (Moze)
5. Vehicles[/color]

## [color=white][b]1. Main formula[/b][/color]

This is the main formula for Amara, Moze and Zane. FL4K also uses it but has a lot of more complicated stuff going on explained in the dedicated section.

> [color=white]CritDMG = [color=dddddd]NormalDMG[/color] [color=00ff00]× 2[/color] × (1 + [color=khaki]SniperBonus[/color]) × (1 + [color=bbff00]WeaponCritBonus[/color]) × (1 + [color=deepskyblue]ManufacturerBonus[/color]) × (1 + [color=violet]Skill[/color] + [color=aaccff]ClassModBonuses[/color] + [color=gold]GuardRank[/color] + [color=orange]AnointA[/color]) × (1 + [color=orange]AnointB[/color])[/color]

[color=dddddd]NormalDMG[/color]: Actual damage dealt when not critting (not damage stated on the item card)

### [color=white]”Multiplicative” bonuses:[/color]
[color=777777]*(for most purposes, calling a bonus just “additive” or “multiplicative” is a misleading oversimplification, but for this formula it’s good enough and it may make it more immediately apparent. It won’t be good enough anymore when we get to FL4K.)*[/color]

[color=00ff00]× 2[/color] : The base critical hit multiplier.

[color=khaki]SniperBonus[/color]: +20% for sniper rifles from all manufacturers. No other weapon type has a modifier. So unlike in BL2:
– no penalty for anything, including assault rifles and alien barrels
– significantly reduced sniper rifle crit dmg (effective x2.4 vs. x4 in BL2 without any other bonuses)
– explosive weapons (rocket launchers, Torgue etc.) do critical hits just like any weapon with normal bullets.

[color=bbff00]WeaponCritBonus[/color]: The crit bonus stated on the item card.
[color=777777]*Note: individual crit dmg parts’ bonuses are also multiplicative among each other, so two +10% parts will result in +21%, not in +20%. The value on the item card is rounded, so e.g. with three +10% parts and one +5% part, the actual bonus is +39.755%, not +40% as stated on the card. This is irrelevant during play but should be considered when testing.*[/color]

[color=deepskyblue]ManufacturerBonus[/color]: Hyperion +5%, Jakobs +10%. Other manufacturers have no bonus.

[color=orange]AnointB[/color]: +25% critical damage while airborne

 

### [color=white]”Additive” bonuses:[/color]

[color=violet]Skill[/color]: The crit bonus from Amara’s [color=white]Transcend[/color] or Moze’s [color=white]Scorching RPM’s[/color].
* Transcend stacks: for example, if you get +27% after one Phasecast shot, if you shoot 2 times with Avatar you’ll get +54%. Fakegrasping doesn’t trigger Transcend, so it can’t be abused that way.

[color=aaccff]ClassMod[/color]: The crit bonus on a class mod, either manufacturer-specific or for all weapons. If you have both on the same class mod, weapons of the manufacturer get the sum of both bonuses.
[color=777777][i]Note: The value on the item card is rounded. I e.g. tried one with “27%” and another one with “13%”, in fact they were about 26.65% and 13.1%. This should be considered when testing.[/i][/color]

[color=gold]GuardRank[/color]: Critical damage guardian rank.

[color=orange]AnointA[/color]:
* +25% critical damage after action skill end
* +60% accuracy and +70% critical damage while Barrier is active (Zane)

+50% critical damage after using Rakk Attack is a whole different story which is explained in the FL4K section.

## [color=white]**2. FL4K**[/color]

Now it gets complicated. Well, not all of it is complicated, so let’s get the “simple” stuff out of the way first:

### [color=white]**2.1 Regular crit bonuses**[/color]

The following skills work like regular crit skills (i.e. like Transcend and Scorching RPM’s):
* [color=white]Ambush Predator[/color]: +4% crit dmg per rank up to +20% when no enemy is close. I estimate the threshold distance is in the ballpark of 10 metres/30 feet (see screenshots at the end of this post). Not boosted by Big Game.
* [color=white]The Most Dangerous Game[/color]: The crit part gives +3.33% crit dmg per rank = +10% with 3/3. [color=ffccaa]Big Game[/color] boosts this: with 3/3 Big Game you’ll get +10% [color=ffccaa]× 1.3[/color] = +13%.
* [color=white]Galactic Shadow[/color]: A flat +15% without surprises. Not boosted by Big Game.
* [color=white]Gunslinger Jabber[/color]: This pet gives +5% crit dmg. It works just like a regular crit skill, also unaffected by Big Game as it’s not in the Hunter tree anyway.

Now what happens in the formula is that all of these are added together. So the “additive” part

> [color=white](1 + [color=violet]Skill[/color] + [color=aaccff]ClassModBonuses[/color] + [color=gold]GuardRank[/color] + [color=orange]AnointA[/color])[/color]

now looks like this:

> [color=white](1 + [color=violet]AmbushPred [color=white]+[/color] [color=violet]DangerousGame [color=ffccaa]× (1 + BigGame)[/color] [color=white]+[/color] GalShadow [color=white]+[/color] GunJabber[/color][/color] + [color=aaccff]ClassModBonuses[/color] + [color=gold]GuardRank[/color] + [color=orange]AnointA[/color])[/color]

Note that calling bonuses simply “additive” or “multiplicative” is beginning to creak here: we have two skills (Big Game and The Most Dangerous Game) multiplied with each other but the product is in the “additive” part. Which gets us to…

 

### [color=white]**2.2 PostAdd crit bonuses**[/color]

FL4K has some “fake” crit bonuses that are added when hitting a crit spot but are [color=ffffff]not part of the main crit formula[/color]. Their damage is based on NormalDMG alone, ignoring other crit bonuses like the ×2 crit base, sniper bonus, weapon crit bonus or anything else in the formulas above. These bonuses are [color=ffffff]Fade Away[/color], [color=ffffff]Hunter’s Eye[/color] (against humans) and the [color=ffffff]+50% crit after Rakk Attack[/color] anointment. They can be thought of as *added after* the regular crit calculation, hence “PostAdd”.

Think of it like this:

> [color=white]CritDMG = [color=dddddd]NormalDMG[/color] × ([color=00ff00]RegularCritStuff[/color] + [color=ff6644]PostAdd1[/color] + [color=ff6644]PostAdd2[/color] + [color=ff6644]PostAdd3[/color])[/color]

Where [color=00ff00]RegularCritStuff[/color] is everything in the main formulas from “× 2” to the end. For example, the Rakk Attack anointment basically adds NormalDMG × 0.5 on top of the “actual” crit damage. One side effect of this is that they’re not reduced by the crit penalty you can get in Mayhem mode.

[color=ff6644]+50% crit after Rakk Attack[/color] anointment: +50% postadd on critical hits after using the Rakk Attack skill. Note that this is much less than it would be if it was a regular crit bonus, as it gets no other crit multiplier, not even the base ×2.

[color=ff6644]Hunter’s Eye[/color]: +6% per rank postadd on crits against humans. They did a better job here at faking crit damage because at least it’s 2 × what’s stated on the card. Hunter’s Eye is also increased by Big Game.

Anomaly: Hunter’s Eye is not triggered by Megavore. Megavore turns a body shot into a crit, except that Hunter’s Eye is ignored so that you get the crit damage of a shot with 0/5 in HE. If Megavore does slightly less damage than an actual crit, this is why.

### **[color=ff6644]Fade Away[/color]**

*First of all thanks to @jafortune for their explanation of https://forums.gearboxsoftware.com/t/the-math-of-fade-away/3704120.*

The in-game discription of Fade Away is misleading because it suggests that simply every hit is a crit now, with no difference where you hit the enemy — but that’s not how it works.
– Fade Away critical damage is different to that of a regular crit.
– Hitting a crit spot does more damage than a body shot, even though “Critical!” will pop up in either case.
– However, all hits count for triggering stuff like Leave no Trace or Jakobs ricochet.

Fade Away adds a damage bonus that works similar to a PostAdd bonus. By default, it adds +200% postadd damage.
* This is reduced to +25% with Guerrillas in the Mist.
* Unblinking Eye adds another 75%, 150%, 225% (and repeat) on consecutive hits on the same enemy. This means your shots get an [i]average[/i] bonus of +350% without Guerrillas and +175% with Guerrillas.

The difference to other postadd bonuses is that it is added on both crit shots and body shots, so it’s basically a flat NormalDMG × FadeAwayBonus added on top of *any* hit. Simply put, it’s:

>[color=white]FadeAwayCritSpotDMG = CritDMG + [color=lightgrey]NormalDMG[/color] × [color=ff6644]FadeAwayBonus[/color][/color]

>[color=white]FadeAwayBodyShotDMG = [color=lightgrey]NormalDMG[/color] × (1 + [color=ff6644]FadeAwayBonus[/color])[/color]

[color=ffffff]Grim Harvest[/color] has no effect on Fade Away.

### [color=ffffff]**Complete FL4K formula**[/color]

If you really want, here’s the entire FL4K formula:

> [color=white]CritDMG = [color=dddddd]NormalDMG[/color] × [[color=00ff00]2[/color] × (1 + [color=khaki]SniperBonus[/color]) × (1 + [color=bbff00]WeaponCritBonus[/color]) × (1 + [color=deepskyblue]ManufacturerBonus[/color]) × (1 + [color=violet]AmbushPred [color=white]+[/color] [color=violet]DangerousGame [color=ffccaa]× (1 + BigGame)[/color] [color=white]+[/color] GalShadow [color=white]+[/color] GunJabber[/color][/color] + [color=aaccff]ClassModBonuses[/color] + [color=gold]GuardRank[/color] + [color=orange]AnointA[/color]) × (1 + [color=orange]AnointB[/color]) [color=ff6644]+ FadeAway + UnblinkingEye + HuntersEye [color=ffccaa]× (1 + BigGame)[/color] + RakkCritAnoint[/color]][/color]

 

## [color=white]**3. Overkill**[/color]

This Guardian Rank reward takes excess damage from the previous kill and adds it to the next shot. The way this works is that it basically takes all the excess damage and adds it to [color=dddddd]NormalDMG[/color] for calculating the next shot.

This means that on critical hits, excess damage will be multiplied along with gun damage for huge damage potential, although there is a cap so that you can’t do more than 5x [color=ffffff]CritDMG[/color] overall. So you can e.g. exploit your excess damage by critting with the Unforgiven, however you’ll quickly run into the cap based on its relatively low gun damage.

See my https://forums.gearboxsoftware.com/t/overkill-explained/4018106 thread for more detail.

 


## [color=white]**4. Pull the Holy Pin (Moze)**[/color]

This gives grenades a crit chance. On crits they just do x2 damage, unaffected by *any* other modifier, so:

> [color=white]GrenadeCritDMG = [color=lightgrey]GrenadeNormalDMG[/color] × [color=00ff00]2[/color][/color]

Critical hits will trigger Redistribution, but it will regenerate gun ammo (not grenades). This skill is unaffected by Mayhem’s critical hit penalty modifier.

## [color=white]**5. Vehicles**[/color]

Same story, crits with vehicle weapons get x2 damage and that’s it. No other crit modifier of any sort applies, also unaffected by Mayhem’s critical hit penalty modifier.

All vehicle weapons can crit, even sticky bombs. The Cyclone’s Needles will get x2 damage on both impact and explosion.

> [color=white]VehicleCritDMG = [color=lightgrey]VehicleNormalDMG[/color] × [color=00ff00]2[/color][/color]

==============

And finally, the screenshots showing the threshold distance for Ambush Predator:

![Photo00010|690×431](upload://o19KYDXExiHv2BPbWC7gHNZju7R.jpeg) ![Photo00011|690×431,100%](upload://n5B3fzeUKCuGf1BeAmBy5fJhnJc.jpeg)

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